**Author details**

Kazimierz Stróż *Faculty of Informatics and Materials Science, University of Silesia, Katowice, Poland* 

## **12. References**


Unique and Effective Characterization of Space Groups in Computer Applications 273


272 Recent Advances in Crystallography

are unsubstantial.

group type is 0,1 or maximum 2.

additional Seitz symbol.

**Author details** 

**12. References** 

22:633-639

Dordrecht: *Cluwer Academic Publishers*

[4] Larson A C (1969) Acta Cryst. A25, S1

*information in three dimensions*, J. Appl. Cryst. 20:532-535

Kazimierz Stróż

From this point of view, such algorithms standardize any SG descriptions and their geometric interpretations and may be treated as an electronic extension of the printed ITA83 tables. In this context the classification of space groups into conventionally versus nonconventionally described, and the evolutionary changes between different editions of Tables

The generation schema based on composition series leads also to a considerable reduction of predefined data, what is an important feature in the implementing and testing of SG derivation programs. Since all the space groups which are based on a given point group are generated in the same way, only the translational parts of generators should be stored. Using small improvements discussed in the text, the non-redundant number of composition series generators is 3, and thus the non-redundant number of translations for each space-

The introduced dual symbol of symmetry operation sheds some light on the lattice properties and thus changes a rather informative character of the geometric symbols into a valuable tool for finding the transformation between different descriptions of the same groups. Since the symbol is universal, convention free, easy to derive and to manipulate on a computer, it is advised to generate space group descriptions simultaneously in two forms, as coordinate triplets and as dual symbols. Any new information can be obtained from the

The simplicity of the considered approach is evident and seems to be valuable also for teaching purposes. Algorithms were implemented in the Visual Basic, in the Excel environment. All procedures need less than 600 programming lines including 200-line subroutine for transforming a symmetry matrix into a dual symbol. This procedure may be also used as stand-alone item to characterize any symmetry matrix. The source code

[1] Han Th ed. (1983) *International Tables for Crystallography* Vol. A. *Space-group Symmetry*,

[2] Abad-Zapatero C, O'Donell T J (1987) *TABLES, a program to display space-group symmetry* 

[3] Sakurai T, Kobayashi K, Horiki T, Furukawa M, Naitou K (1989) *CRYST – a system to display 3D images of crystal structure, symmetry operations and crystal forms,* J. Appl. Cryst.

included in the Excel worksheet may be obtained from the author on request.

*Faculty of Informatics and Materials Science, University of Silesia, Katowice, Poland* 

	- [28] Sands D E (1982) *Vectors and tensors in crystallography*, Massachusetts: Addison-Wesley Publishing Company
